> I don't think David was trying to generalize the successor
> relation in the sense of finding a "moral equivalent" in a poset for
> the natural numbers' successor _function_. All he wants - I think -
> is a notation for "a > b and there is no a>c>b". I would suggest
> using an indefinite article with a noun formation:
>
> " a is _a_ successor of b"
>
> or a prepositional formation that does not connote uniqueness or
> necessary existence:
>
> "a is immediately above b"
>
> Bob Pare and I used "<!" for this in our 1993 paper on tileorders.
In that case I believe there is established terminology/notation in
lattice theory, they say "a covers b", denoted b -< a, and corresponding
intervals (i.e. intervals with [a,b]={a,b}) are called gaps.
Mamuka